Skip to main content
Log in

Unification in Boolean rings

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript


We show that two Boolean terms which are unifiable have a most general unifier, which can be described using the terms themselves and a single unifier. Techniques for finding a single unifier are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. Boole, G., The Mathematical Analysis of Logic, Macmillan 1847. Reprinted B. Blackwell (1948).

  2. Büttner, W., Simonis, H., ‘Embedding Boolean expressions into Logic Programming’, preprint, to appear in Journal of Symbolic Computation (1987).

  3. Hailpern, T., Boole's Logic and Probability, North-Holland (1986).

  4. Herbrand, J., ‘Investigations in Proof Theory’, [Herbrand's thesis] in Jacques Herbrand Logical Writings, ed. W. Goldfarb, pp. 44–202. D. Reidel (1971).

  5. Herstein, I. N., ‘Non-commutative rings’, Carus Mathematical Monograph, Wiley (1968).

  6. Herold, A., ‘Combination of Unification Algorithms’, in 8th International Conference on Automated Deduction, Lecture Notes in Computer Science 230, pp. 450–469. Springer (1986).

  7. Hsiang, J., ‘Rewrite rules for clausal and non-clausal theorem proving’, in Proc. 10th ICALP, LNCS 154 (1983).

  8. Hsiang, J., ‘Refutational Theorem Proving using Term-Rewriting Systems’, Artificial Intelligence 25 (1985).

  9. Kapur, D., Narendran, P., ‘An equational approach to theorem proving in the first order predicate calculus’, Proc. IJCAI 85, Los Angeles (1985).

  10. Löwenheim, L., Über das Auflösungproblem im logischen Klassenkalkül’, Sitzungber. Berl. Math. Gesell. 7, 89–94 (1908).

    Google Scholar 

  11. Martin, U., Nipkow, T., ‘Unification in Boolean Rings’, in 8th International Conference on Automated Deduction, Lecture Notes in Computer Science 230, pp. 506–513. Springer (1986).

  12. Martin, U., Nipkow, T., ‘Boolean Unification — A Survey’, to appear in Journal of Symbolic Computation.

  13. Monk, J. D., Mathematical Logic, Springer (1976).

  14. Robinson, J. A., ‘A machine oriented logic based on the resolution principle’, J.ACM 12, 23–41 (1974).

    Google Scholar 

  15. Rudeanu, S., Boolean functions and equations, North Holland (1974).

  16. Siekmann, J. H., ‘Universal Unification’, in Proceedings of European Conference on Artificial Intelligence, Brighton (1986).

  17. Schröder, E., ‘Vorlesungen über die Algebra der Logic, (Leipzig, Vol. 1, 1890; Vol. 2, 1891, 1905; Vol. 3, 1895). Reprint Chelsea, Bronx, NY. (1966).

  18. Vitter, J. S., Simons, R. A., ‘New Classes for Parallel Complexity: A Study of Unification and Other Complete Problems for P’, IEEE Transactions on Computers, 403–418 (1986).

  19. Watts, D. E., Cohen, J. K., ‘Computer-Implemented Set Theory’, Amer. Math. Month. 87 (1980).

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Martin, U., Nipkow, T. Unification in Boolean rings. J Autom Reasoning 4, 381–396 (1988).

Download citation

  • Received:

  • Issue Date:

  • DOI:

Key words